{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true,
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "控制饮食情况下的正常代谢\n",
      "[99.875, 99.628125, 99.262421875, 98.780861328125, 98.18633979492188, 97.48168130004883, 96.66963926754761, 95.75289828585892, 94.73407582871245, 93.61572393299464]\n",
      "k=33时,w(33)=74.9888\n",
      "控制饮食+大量运动后的变化\n",
      "[99.375, 98.64375, 97.8094375, 96.875154375, 95.84389974374999, 94.71858275143748, 93.50202526889436, 92.19696451082753, 90.8060555755027, 89.33187390823761]\n",
      "k=23时,w(23)=74.7388\n",
      "控制饮食+适量运动后的变化\n",
      "[99.625, 99.1353125, 98.53409140625, 97.82440389257813, 97.00923278553223, 96.0914788839301, 95.07396321462203, 93.95942922621992, 92.75054492249888, 91.44990493713016]\n",
      "k=27时,w(27)=74.8952\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#13.1\n",
    "\n",
    "'''\n",
    "不满足\n",
    "在只进行饮食控制，不进行运动时，可以满足；但是需要进行运动控制\n",
    "要求每周体重减少不超过1kg，主要控制运动量\n",
    "体重变化依然正比于吸收的热量，a = 1/8000\n",
    "可知代谢消耗系数依然未变 B = 0.025\n",
    "'''\n",
    "'''\n",
    "题目并没有表达清楚！\n",
    "其实题目本意是两种控制方法：1、只控制饮食，2、控制饮食+运动\n",
    "'''\n",
    "'''\n",
    "可以将yt改为20，B+ayt = 0.025+20/8000=0.0275\n",
    "最终第一阶段的体重末值为91.4499，平均下降不到1kg\n",
    "但是最终需要增加4天控制才能减肥成功\n",
    "'''\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rc('font', family='SimHei'); plt.rc('font',size=16)\n",
    "def fun(delta,*s):\n",
    "    w=100; tw=[]\n",
    "    for k in range(1,11):\n",
    "        w=delta*w+2.5-0.125*k; tw.append(w)\n",
    "    print(tw); w2=tw[-1]  #提取第二阶段的初值\n",
    "    tw2=[];k =11\n",
    "    while w2>=75:\n",
    "        k+=1; w2=delta*w2+1.25;\n",
    "        tw2.append(w2); tw.append(w2)\n",
    "    print(\"k=%d时,w(%d)=%.4f\"%(k,k,w2))\n",
    "    plt.plot(np.arange(1,len(tw)+1),tw,s[0])  #传入的s是tuple类型\n",
    "\n",
    "print('控制饮食情况下的正常代谢')\n",
    "fun(0.975,\"s-\")\n",
    "print('控制饮食+大量运动后的变化')\n",
    "fun(0.97,\"-\")\n",
    "print('控制饮食+适量运动后的变化')\n",
    "fun(0.9725,\"*-\")\n",
    "plt.legend((\"正常代谢\",\"大量运动\",\"适量运动\"))\n",
    "plt.xlabel(\"$k$/周\"); plt.ylabel(\"$w$/kg\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "C0*(r + 1)**n - b/r\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 4 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#13.2\n",
    "\n",
    "'''\n",
    "主要分析平衡点和稳定性\n",
    "题中方程无法求特解\n",
    "'''\n",
    "'''\n",
    "x(k+1)-(1+r)x(k)=b\n",
    "假设k=a是平衡点，则x(a)=-b/r\n",
    "方程的通解为x(k)=C*(1+r)**k-b/r,r != 0;x(k) = C+bt,r =0\n",
    "因为规定r和b是非零常数，所以最终方程的通解为x(k)=C*(1+r)**k-b/r\n",
    "'''\n",
    "'''\n",
    "最终发现，从长远角度来看，r值对最终的函数值具有重要影响，b的值从长远角度而言并没有对函数值有太大的影响\n",
    "最终函数都有相应的转折点（平衡点）\n",
    "'''\n",
    "#将r，b看作变量\n",
    "import sympy as sym\n",
    "import matplotlib.pyplot as plt\n",
    "from sympy.abc import n\n",
    "r,b = sym.symbols('r b', real = True, constant = True,Nonzero = True)\n",
    "x = sym.Function('x')\n",
    "f = x(n+1)-(1+r)*x(n)-b\n",
    "ff = sym.rsolve(f,x(n))\n",
    "print(ff)\n",
    "#假定c0 = 1或者-1\n",
    "#c0 = 1\n",
    "ax1 = plt.subplot(221)\n",
    "ax2 = plt.subplot(222)\n",
    "ax3 = plt.subplot(223)\n",
    "ax4 = plt.subplot(224)\n",
    "for i in [-5,-4,-3,-2,2,3,4,5]:\n",
    "    r = i\n",
    "    for j in [5]:\n",
    "        b = j\n",
    "        func = lambda k:(1+r)**k-b/r\n",
    "        value = []\n",
    "        for k in range(-6,6):\n",
    "            value.append(func(k))\n",
    "        ax1.plot(range(-6,6),value)\n",
    "for i in [-5,-4,-3,-2,2,3,4,5]:\n",
    "    r = i\n",
    "    for j in [-5]:\n",
    "        b = j\n",
    "        func = lambda k:(1+r)**k-b/r\n",
    "        value = []\n",
    "        for k in range(-6,6):\n",
    "            value.append(func(k))\n",
    "        ax2.plot(range(-6,6),value)\n",
    "#c0 = -1\n",
    "for i in [-5,-4,-3,-2,2,3,4,5]:\n",
    "    r = i\n",
    "    for j in [5]:\n",
    "        b = j\n",
    "        func = lambda k:-((1+r)**k-b/r)\n",
    "        value = []\n",
    "        for k in range(-6,6):\n",
    "            value.append(func(k))\n",
    "        ax3.plot(range(-6,6),value)\n",
    "for i in [-5,-4,-3,-2,2,3,4,5]:\n",
    "    r = i\n",
    "    for j in [-5]:\n",
    "        b = j\n",
    "        func = lambda k:-((1+r)**k-b/r)\n",
    "        value = []\n",
    "        for k in range(-6,6):\n",
    "            value.append(func(k))\n",
    "        ax4.plot(range(-6,6),value)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "问题1 **********\n",
      "C0*(r + 1)**k\n",
      "较好自然环境下数量变化为： [102, 103, 105, 107, 109, 111, 112, 114, 116, 118, 120, 122, 124, 126, 128, 131, 133, 135, 137, 140, 142, 144, 147, 149, 152]\n",
      "中等自然环境下数量变化为： [101, 101, 102, 102, 103, 103, 104, 104, 105, 106, 106, 107, 107, 108, 109, 109, 110, 110, 111, 112, 112, 113, 113, 114, 115]\n",
      "较差自然环境下数量变化为： [96, 91, 87, 83, 79, 76, 72, 69, 66, 63, 60, 58, 55, 52, 50, 48, 46, 44, 42, 40, 38, 36, 35, 33, 32]\n",
      "问题2 **********\n",
      "C0*(r + 1)**k + 3/r\n",
      "较好自然环境下数量变化为： [99, 97, 96, 95, 93, 92, 90, 89, 87, 86, 84, 83, 81, 79, 78, 76, 74, 73, 71, 69, 67, 65, 63, 61, 59]\n",
      "中等自然环境下数量变化为： [98, 95, 93, 90, 88, 85, 83, 80, 77, 75, 72, 70, 67, 64, 62, 59, 56, 54, 51, 48, 46, 43, 40, 37, 35]\n",
      "较差自然环境下数量变化为： [92, 85, 78, 72, 66, 60, 54, 49, 43, 39, 34, 29, 25, 21, 17, 13, 10, 6, 3, 0, -3, -6, -9, -11, -14]\n",
      "问题3 **********\n"
     ]
    },
    {
     "data": {
      "text/plain": "'\\n由于问题1可知，在较好及中等环境下，山猫的数量呈几何级数无限增长\\n令x(k+1)=x(k),即可以求出平衡点 x= -b/r\\n则每年人工繁殖b = -60*（-0.045）=2.7，则取整为3只\\n所以最终需要人工繁殖3只，可以将种群稳定在60附近\\n'"
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 2 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#13.3\n",
    "\n",
    "'''\n",
    "总体可列出公式x(k+1)=(1+r)*x(k),k = 0,1,2...\n",
    "c0 = x0 = 100\n",
    "'''\n",
    "\n",
    "import numpy as np\n",
    "import sympy as sym\n",
    "import matplotlib.pyplot as plt\n",
    "from sympy.abc import k\n",
    "r = sym.symbols('r', real = True, constant = True)\n",
    "x = sym.Function('x')\n",
    "ax1 = plt.subplot(211)\n",
    "ax2 = plt.subplot(212)\n",
    "print('问题1','*'*10)\n",
    "\n",
    "#问题1\n",
    "'''\n",
    "问题1：在25年内较好和中等环境下都在稳定增长数量趋于无穷，较差环境下数量下降趋于0\n",
    "'''\n",
    "f = x(k+1)-(1+r)*x(k)\n",
    "ff = sym.rsolve(f,x(k))\n",
    "print(ff)#查看解的情况\n",
    "func = lambda r,k:100*(1+r)**k\n",
    "listr = [0.0168,0.0055,-0.045]\n",
    "for i in listr:\n",
    "    mount = []\n",
    "    for j in range(1,26):\n",
    "        mount.append(func(i,j))\n",
    "    if i == listr[0]:\n",
    "        ax1.plot(range(1,26),mount,label = '较好自然环境')\n",
    "        print('较好自然环境下数量变化为：',[int(np.round(i,0)) for i in mount])\n",
    "    elif i == listr[1]:\n",
    "        ax1.plot(range(1,26),mount,label = '中等自然环境')\n",
    "        print('中等自然环境下数量变化为：',[int(np.round(i,0)) for i in mount])\n",
    "    else:\n",
    "        ax1.plot(range(1,26),mount,label = '较差自然环境')\n",
    "        print('较差自然环境下数量变化为：',[int(np.round(i,0)) for i in mount])\n",
    "ax1.legend(loc = 'best')\n",
    "plt.rc('font',size = 6);plt.rc('font',family = 'SimHei')\n",
    "\n",
    "#问题2\n",
    "'''\n",
    "问题2：在25年内数量都会下降趋于0，较差环境下该物种在25年内会灭绝\n",
    "利用sympy求方程解时，发现有问题，最终根据人工算出来的解进行计算\n",
    "'''\n",
    "print('问题2','*'*10)\n",
    "f2 = x(k+1)-(1+r)*x(k)+3\n",
    "ff2 = sym.rsolve(f2,x(k))\n",
    "print(ff2)#查看解的情况\n",
    "func2 = lambda r,k:100*(1+r)**k+3/r*(1-(1+r)**k)\n",
    "listr2 = [0.0168,0.0055,-0.045]\n",
    "for i in listr2:\n",
    "    mount2 = []\n",
    "    for j in range(1,26):\n",
    "        mount2.append(func2(i,j))\n",
    "    if i == listr2[0]:\n",
    "        ax2.plot(range(1,26),mount2,label = '较好自然环境')\n",
    "        print('较好自然环境下数量变化为：',[int(np.round(i,0)) for i in mount2])\n",
    "    elif i == listr2[1]:\n",
    "        ax2.plot(range(1,26),mount2,label = '中等自然环境')\n",
    "        print('中等自然环境下数量变化为：',[int(np.round(i,0)) for i in mount2])\n",
    "    else:\n",
    "        ax2.plot(range(1,26),mount2,label = '较差自然环境')\n",
    "        print('较差自然环境下数量变化为：',[int(np.round(i,0)) for i in mount2])\n",
    "ax2.legend(loc = 'best')\n",
    "\n",
    "#问题3\n",
    "print('问题3','*'*10)\n",
    "'''\n",
    "由于问题1可知，在较好及中等环境下，山猫的数量呈几何级数无限增长\n",
    "令x(k+1)=x(k),即可以求出平衡点 x= -b/r\n",
    "则每年人工繁殖b = -60*（-0.045）=2.7，则取整为3只\n",
    "所以最终需要人工繁殖3只，可以将种群稳定在60附近\n",
    "'''"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "可供老人使用119个月,约9.916666666666666年\n",
      "[99299.99999999999, 98597.89999999998, 97893.69369999997, 97187.37478109996, 96478.93690544325, 95768.37371615956, 95055.67883730803, 94340.84587381996, 93623.8684114414, 92904.74001667571, 92183.45423672574, 91460.00459943591, 90734.3846132342, 90006.5877670739, 89276.60753037511, 88544.43735296623, 87810.07066502511, 87073.50087702017, 86334.72137965122, 85593.72554379016, 84850.50672042153, 84105.05824058279, 83357.37341530452, 82607.44553555043, 81855.26787215707, 81100.83367577354, 80344.13617680085, 79585.16858533124, 78823.92409108722, 78060.39586336048, 77294.57705095055, 76526.4607821034, 75756.0401644497, 74983.30828494305, 74208.25820979787, 73430.88298442725, 72651.17563338052, 71869.12916028066, 71084.7365477615, 70297.99075740477, 69508.88472967698, 68717.41138386601, 67923.56361801761, 67127.33430887165, 66328.71631179826, 65527.70246073365, 64724.28556811584, 63918.45842482018, 63110.213800094636, 62299.544441494916, 61486.44307481939, 60670.902404043845, 59852.91511125597, 59032.473856589735, 58209.5712781595, 57384.19999199397, 56556.352591969946, 55726.02164974585, 54893.19971469508, 54057.87931383916, 53220.05295178067, 52379.71311063601, 51536.85224996791, 50691.462806717806, 49843.53719513796, 48993.06780672337, 48140.047010143535, 47284.46715117396, 46426.320552627476, 45565.59951428535, 44702.2963128282, 43836.403201766676, 42967.91241137197, 42096.816148606085, 41223.1065970519, 40346.77591684305, 39467.816244593574, 38586.21969332735, 37701.97835240733, 36815.084287464546, 35925.529540326934, 35033.30612894791, 34138.40604733475, 33240.82126547675, 32340.543729273173, 31437.56536046099, 30531.87805654237, 29623.473690711995, 28712.34411178413, 27798.481144119476, 26881.876587551833, 25962.522217314487, 25040.40978396643, 24115.531013318327, 23187.877606358277, 22257.44123917735, 21324.21356289488, 20388.186203583566, 19449.350762194314, 18507.698814480893, 17563.221910924334, 16615.911576657105, 15665.759311387075, 14712.756589321234, 13756.894859089196, 12798.165543666462, 11836.56004029746, 10872.06972041835, 9904.685929579604, 8934.399987368342, 7961.203187330446, 6985.086796892437, 6006.0420572831135, 5024.0601834549625, 4039.132364005327, 3051.2497610973423, 2060.403510380634, 1066.5847209117755, 69.78447507451074]\n",
      "需要存170907.60592826287\n"
     ]
    }
   ],
   "source": [
    "#13.4\n",
    "\n",
    "'''\n",
    "标准的差分方程模型\n",
    "A(k+1)=(1+r)*A(k)-b，求解得A(k)=A(0)*(1+r)**k+b/r(1-(1+r)**k)\n",
    "需求：1、计算A(k)=0的时间 2、每月支出1000元，在月利率0.3%的情况下，使用至80岁\n",
    "'''\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rc('font',family = 'SimHei')\n",
    "#问题1 要求A(k)=0\n",
    "a = 100000\n",
    "yue = []\n",
    "r = 0.003\n",
    "b = 1000\n",
    "for i in range(1,1000):\n",
    "    a = (1+r)*a-b\n",
    "    yue.append(a)\n",
    "    if a<1000:\n",
    "        print('可供老人使用{}个月,约{}年'.format(i,i/12))\n",
    "        print(yue)\n",
    "        break\n",
    "    else:\n",
    "        continue\n",
    "#问题2 要求用到60岁n=(80-60)*12=240,即要求A(240) = 0\n",
    "cunkuan = 1000*((1+0.003)**240-1)/(0.003*(1+0.003)**240)\n",
    "print('需要存{}元'.format(cunkuan))"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "outputs": [],
   "source": [
    "#13.5\n",
    "\n",
    "'''\n",
    "S(n+1) = y%*I(n)+(1-z%)*S(n)\n",
    "I(n+1) = z%*s(n)+(1-x%)I(n)\n",
    "R(n+1) = y%*I(n)\n",
    "'''\n",
    "#题目并没有给出相应的x，y，z的值\n",
    "#参考相应的文档，最终健康和患者人数应该是稳定的状态"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TX= [[   35.2           33.44          31.768         37.1492\n",
      "     41.91286       46.107281      51.15745855    56.8983319\n",
      "     63.18265695    70.15270089    77.91093556    86.52555486\n",
      "     96.08951189   106.71140154   118.50789133   131.60822011\n",
      "    146.15666661   162.31339577   180.25615356   200.18236587\n",
      "    222.31129994   246.88645335   274.17823912   304.48696455\n",
      "    338.14613409   375.52611873   417.03823178   463.13925474\n",
      "    514.33646351   571.19321023   634.33512215   704.45698582\n",
      "    782.33039215   868.81222673   964.85409859  1071.5128113\n",
      "   1189.96199163  1321.50500357  1467.58929003  1629.82229987\n",
      "   1809.98917558  2010.07239623  2232.27359179  2479.03776897\n",
      "   2753.08021497  3057.4163754   3395.39503489  3770.73516571\n",
      "   4187.56684975  4650.47672417]\n",
      " [    0.            21.12          20.064         19.0608\n",
      "     22.28952       25.147716      27.6643686     30.69447513\n",
      "     34.13899914    37.90959417    42.09162053    46.74656134\n",
      "     51.91533292    57.65370714    64.02684092    71.1047348\n",
      "     78.96493207    87.69399997    97.38803746   108.15369214\n",
      "    120.10941952   133.38677996   148.13187201   164.50694347\n",
      "    182.69217873   202.88768045   225.31567124   250.22293907\n",
      "    277.88355284   308.60187811   342.71592614   380.60107329\n",
      "    422.67419149   469.39823529   521.28733604   578.91245915\n",
      "    642.90768678   713.97719498   792.90300214   880.55357402\n",
      "    977.89337992  1085.99350535  1206.04343774  1339.36415508\n",
      "   1487.42266138  1651.84812898  1834.44982524  2037.23702093\n",
      "   2262.44109942  2512.54010985]\n",
      " [   76.            72.2           84.43          95.2565\n",
      "    104.789275     116.26695125   129.31439069   143.5969476\n",
      "    159.43795657   177.0703081    196.64898832   218.3852543\n",
      "    242.52591259   269.33611665   299.10959117   332.1742423\n",
      "    368.89408129   409.67307627   454.95992243   505.25295441\n",
      "    561.10557579   623.13236164   692.01582853   768.51394111\n",
      "    853.46845166   947.81416313  1052.58921531  1168.94650797\n",
      "   1298.16638688  1441.67073216  1601.03860413  1778.02361853\n",
      "   1974.57324257  2192.85022406  2435.25638933  2704.45907189\n",
      "   3003.42046266  3335.43020461  3704.14159062  4113.61176269\n",
      "   4568.34635507  5073.34907226  5634.17674766  6257.00048858\n",
      "   6948.67358046  7716.80689747  8569.85264934  9517.1973858\n",
      "  10569.26528221 11737.63284267]\n",
      " [   36.8           34.96          33.212         38.8378\n",
      "     43.81799       48.2030665     53.48279758    59.48461972\n",
      "     66.0545959     73.34146002    81.45234173    90.45853463\n",
      "    100.45721698   111.56191979   123.89461366   137.59041194\n",
      "    152.80015146   169.69127739   188.44961509   209.28156432\n",
      "    232.41635903   258.10856486   286.64088636   318.32728112\n",
      "    353.51641291   392.59548776   435.99451504   484.19103904\n",
      "    537.71539367   597.15653796   663.1685368    736.4777579\n",
      "    817.89086452   908.30369158  1008.71110307  1120.21793909\n",
      "   1244.05117307  1381.57341282  1534.29789412  1703.90513168\n",
      "   1892.26141084  2101.43932333  2333.74057324  2591.72130392\n",
      "   2878.22022475  3196.38984701  3549.73117284  3942.13221869\n",
      "   4377.91079747  4861.86202982]\n",
      " [    0.            22.08          20.976         19.9272\n",
      "     23.30268       26.290794      28.9218399     32.08967855\n",
      "     35.69077183    39.63275754    44.00487601    48.87140504\n",
      "     54.27512078    60.27433019    66.93715188    74.3367682\n",
      "     82.55424716    91.68009088   101.81476643   113.06976905\n",
      "    125.56893859   139.44981542   154.86513892   171.98453181\n",
      "    190.99636867   212.10984775   235.55729266   261.59670902\n",
      "    290.51462343   322.6292362    358.29392278   397.90112208\n",
      "    441.88665474   490.73451871   544.98221495   605.22666184\n",
      "    672.13076345   746.43070384   828.94404769   920.57873647\n",
      "   1022.34307901  1135.3568465   1260.863594    1400.24434394\n",
      "   1555.03278235  1726.93213485  1917.83390821  2129.8387037\n",
      "   2365.27933122  2626.74647848]\n",
      " [   19.            18.05          33.7075        47.754125\n",
      "     60.31181875    74.77323781    90.75267142   107.90641778\n",
      "    126.5783558    147.01751688   169.39120919   193.92530574\n",
      "    220.88259423   250.5448051    283.22331248   319.26501077\n",
      "    359.05433638   403.01730493   451.62650784   505.40625727\n",
      "    564.9382712    630.86806158   703.91202006   784.86527325\n",
      "    874.61040845   974.12716453  1084.50319211  1206.946002\n",
      "   1342.79623367  1493.54238956  1660.83719723  1846.51577945\n",
      "   2052.61583204  2281.40003149  2535.38091895  2817.34853422\n",
      "   3130.40110389  3477.97912128  3863.9031931   4292.41606921\n",
      "   4768.22931811  5296.57516146  5883.26403826  6534.74853185\n",
      "   7258.19436322  8061.55923182  8953.68037137  9944.37178395\n",
      "  11044.53222253 12266.26510982]]\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
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    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "特征值= [ 0.95      +0.j          0.        +0.j          0.        +0.j\n",
      "  1.11054388+0.j         -0.08027194+0.41454485j -0.08027194-0.41454485j] \n",
      "特征向量为：\n",
      " [[ 0.00000000e+000+0.00000000e+00j  0.00000000e+000+0.00000000e+00j\n",
      "   0.00000000e+000+0.00000000e+00j -2.49711587e-001+0.00000000e+00j\n",
      "  -6.62008564e-002+3.41878181e-01j -6.62008564e-002-3.41878181e-01j]\n",
      " [ 0.00000000e+000+0.00000000e+00j  0.00000000e+000+0.00000000e+00j\n",
      "   0.00000000e+000+0.00000000e+00j -1.34913131e-001+0.00000000e+00j\n",
      "   4.94824401e-001-1.45716772e-16j  4.94824401e-001+1.45716772e-16j]\n",
      " [ 0.00000000e+000+0.00000000e+00j  0.00000000e+000+0.00000000e+00j\n",
      "   0.00000000e+000+0.00000000e+00j -6.30262895e-001+0.00000000e+00j\n",
      "  -3.10022203e-001-1.24741929e-01j -3.10022203e-001+1.24741929e-01j]\n",
      " [ 0.00000000e+000+0.00000000e+00j  0.00000000e+000+0.00000000e+00j\n",
      "   7.86518602e-292+0.00000000e+00j -2.61062113e-001+0.00000000e+00j\n",
      "  -6.92099862e-002+3.57418098e-01j -6.92099862e-002-3.57418098e-01j]\n",
      " [ 0.00000000e+000+0.00000000e+00j  7.84882766e-001+0.00000000e+00j\n",
      "  -7.84882766e-001+0.00000000e+00j -1.41045547e-001+0.00000000e+00j\n",
      "   5.17316419e-001+0.00000000e+00j  5.17316419e-001-0.00000000e+00j]\n",
      " [ 1.00000000e+000+0.00000000e+00j -6.19644289e-001+0.00000000e+00j\n",
      "   6.19644289e-001+0.00000000e+00j -6.58911208e-001+0.00000000e+00j\n",
      "  -3.24114121e-001-1.30412016e-01j -3.24114121e-001+1.30412016e-01j]] \n",
      "c= 2.9274590657712317e+277\n",
      "[4650.476724172188, 2512.5401098512593, 11737.632842667654, 4861.862029816379, 2626.746478480862, 12266.265109816757]\n"
     ]
    },
    {
     "data": {
      "text/plain": "<BarContainer object of 6 artists>"
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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   ],
   "source": [
    "#13.6\n",
    "\n",
    "'''\n",
    "该种群变化的原因就在于母牛每年生育0.44头雌性，0.46头雄性\n",
    "x(t)=[x1(t),x2(t),x3(t)]表示各阶段雌性野牛分布情况\n",
    "y(t)=[y1(t),y2(t),y3(t)]表示各阶段雄性野牛分布情况\n",
    "z(t)=[x1(t),x2(t),x3(t),y1(t),y2(t),y3(t)]表示t时刻各年龄组雌雄性分布情况\n",
    "z(t+1)=pz(t),z(0) = [0,0,80,0,0,20]\n",
    "'''\n",
    "'''\n",
    "x1(t+1)=0.44*x3(t)\n",
    "x2(t+1)=0.6*x1(t)\n",
    "x3(t+1)=0.75*x2(t)+0.95*x3(t)\n",
    "y1(t+1)=0.46x3(t)\n",
    "y2(t+1)=0.6y1(t)\n",
    "y3(t+1)=0.75*y2(t)+0.95*y3(t)\n",
    "'''\n",
    "'''\n",
    "最终成年公牛和成年母牛数量不断稳定，并且各个整体趋势都是不断增加\n",
    "'''\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "p = np.array([[0,0,0.44,0,0,0],\n",
    "              [0.6,0,0,0,0,0],\n",
    "              [0,0.75,0.95,0,0,0],\n",
    "              [0,0,0.46,0,0,0],\n",
    "              [0,0,0,0.6,0,0],\n",
    "              [0,0,0,0,0.75,0.95]])\n",
    "x=np.array([0,0,80,0,0,20])\n",
    "TX=np.zeros((6,50))\n",
    "for i in range(50):\n",
    "    x=p.dot(x)\n",
    "    TX[:,i]=x.flatten()\n",
    "print(\"TX=\",TX)\n",
    "labelniu = ['公牛牛犊','公牛小牛','公牛成年牛','母牛牛犊','母牛小牛','母牛成年牛']\n",
    "for i in range(6):\n",
    "    plt.plot(TX[i],label = labelniu[i] )\n",
    "plt.legend(loc = 'best',fontsize = 12)\n",
    "plt.show()\n",
    "val,vec = np.linalg.eig(p)#计算特征值和特征向量\n",
    "cv=(np.linalg.inv(vec)).dot(x); c=abs(cv[0])\n",
    "print(\"特征值=\",val,\"\\n特征向量为：\\n\",vec,'\\nc=',c)\n",
    "fenbu = list(TX[:,49])\n",
    "print(fenbu)\n",
    "plt.bar(labelniu,fenbu)"
   ],
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